Archer, commonly known as Stuart, was born in Hampstead on 3rd February 1915, the son of Bertram George Reine Archer and Francis Maud Hatfield. After attending Sheringham House school in Hampstead, Archer went on to Regent's Street Polytechnic. He qualified as an Associate of the Royal Institute of British Architects at the youngest age permitted, at 21, in July 1936. He worked in Gray's Inn, initially with Ingram Son and Archer. He continued working with this partnership throughout his working life except for his time in the Army.

In 1937, he joined The Honorable Artillery Company T.A. as a private soldier moving onto the Officer Cadet Training Unit of 142 Royal Engineers from October 1939 to January 1940. He married Kathleen Matilda Hatt in 1939 and they had one son (Ian Stuart Trevelyan) and two daughters (Deidre and Melanie).

He was commissioned as a 2nd Lieutenant in January 1940 and was posted to 553 Field Company Royal Engineers being appointed Officer in Charge of 104 Bomb Disposal Section a fe months later stationed in Cardiff. Between June 1940 and September 1940 he dealt with over 200 bombs. On 2nd September 1940 he dealt with a number of unexploded devices at Llandarcy, near Swansea, which saw him awarded the GC. He was invested with the GC in October 1941 at Buckingham Palace.

After demobilisation, he retunred to his career as an architect. For many years he designed pubs for different breweries one of which was the Cricketers at Mitcham Common. In 1950 he re-joined the Army Emergency Reserve. In 1953 he was selected to command No 142 Bomb Disposal Regiment as a Lt.Colonel. Archer was appointed Honorary Colonel Bomb Disposal Regiments in 1963. He was elected as a Fellow of the Royal Institute of British Architects in 1970.

In the late 1980s Archer's son Ian, joined the partnership which became Archer & Son. He finally retired in 1995 just after he became the Chairman of the VC and GC Association. He held the position until 2006. He was also a Freemason (since 1939) and held the Grand Lodge Officer role in later life.

On 3rd February 2015, Archer became the only VC or GC (to date) to reach the age of 100. Sadly, he passed away just three months later on 3rd May. He was cremated at the New Southgate Crematorium.